You have to press or tap the home button to bring up the password screen. It you have Touch ID set up, placing your finger on the Touch ID sensor will unlock the iPhone without the password screen showing up.
How to get to the password screen changed in iOS 10. You now press the home button to get to the password screen. The iPhone 4S can’t be updated past iOS 9.3.5 and you can still swipe to the right to get to the password screen.